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Augmented Models in Estimation and Control


U. Mäder


The field of automatic control has seen tremendous advances in the past years, driven by the increasing availability of capable computers for small and embedded systems with tight constraints on cost, energy and size. Sophisticated nonlinear filters such as the Extended Kalman Filter can be run even on average embedded hardware, and complex optimizing control schemes such as Model Predictive Control can be precomputed and thus executed on tiny systems in real time. Despite the availability of promising new theories and algorithms, the practitioner often finds it hard to apply these methods to the problems at hand. One of the problems lies in the fact that the theoretical frameworks are relatively involved, rendering the adaptation of many theoretical algorithms to practical problems difficult. Many estimation and control algorithms employ a dynamical model of the system under consideration. Augmented models are a promising tools for extending such algorithms to fit practical problems. Augmenting a model thereby describes the act of appending additional dynamics to an already existing model of the system. These augmented dynamics may for instance represent disturbances acting on the system, or they may be used to model varying parameters of the dynamic equations of the system. The advantage of augmented models is that they do not conceptually change the underlying algorithm, thus retaining most or all of its properties. This thesis strives to give an overview of the uses of augmented models in estimation and control, and to provide several methods which facilitate the adaptation of existing algorithms to practical problems. In the first part, preliminaries necessary to understand the text are established. In the second part, two case studies are presented demonstrating the usefulness of augmented models in estimation. The first study is concerned with attitude detection of vehicles with low-cost sensors. A sensor box is fitted to the vehicle comprising a GPS receiver and an accelerometer. The orientation of the box with respect to the vehicle is unknown and has thus to be inferred from the measurements. The lack of gyros (turn rate sensors) further complicates the task. An Extended Kalman Filter (EKF) is employed, where the equations of motion of the vehicle are augmented by the installation angles. This approach is shown to reliably produce correct estimates both in simulation and experimental trials. A second case study revolves around a collision avoidance system for light aircraft. The system uses GPS measurements to continuously compute a prediction of the aircraft trajectory, which is then transmitted by means of a digital radio link. For the system to work correctly, the prediction needs to be accurate. The current implementation does not account for wind, thus showing significant prediction error when strong wind disturbances are encountered. We show that by employing a dynamical model of the aircraft, augmented by a wind model and then using an Interacting Multiple Models (IMM) filter, a high prediction accuracy can be attained also in windy conditions. The method has been validated experimentally by using a large database of flight records of gliders. The third part is dedicated to reference tracking with Model Predictive Control. In many practical control applications, a design goal is to remove tracking offset in presence of persistent disturbances and model mismatch. Classical control methods such as PID achieve this by explicitly adding integral action on the tracking error, which automatically eliminates offset in the steady-state. In the MPC framework, this approach does not provide an adequate solution since windup issues may arise when constraints on the input or the state vector are present. We tackle the problem by employing model augmentation, where a disturbance model captures the effects of model mismatch and disturbances. An observer is used to estimate the disturbance, a target state is computed from the disturbance estimate and the reference, and the MPC formulation is extended to penalize the deviation from this target state. We first treat the case where the system state is measurable and no model mismatch is present, termed the nominal case. This case is motivated by an inverted pendulum benchmark problem. We move on by considering offset-free control with linear models and constant reference signals. The method is then extended to signals generated by arbitrary unstable linear dynamics, such as ramps or sinusoids. Finally, we extend the concept to nonlinear models, yielding the most general form of conditions for offset-free control. For all these cases, we present concise and sufficient conditions for zero offset.


Type of Publication:

(03)Ph.D. Thesis

M. Morari

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% Autogenerated BibTeX entry
@PhDThesis { Xxx:2010:IFA_4025,
    author={U. M{\"a}der},
    title={{Augmented Models in Estimation and Control}},
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